package twice.class_matrix;

public class Class01_FibonacciProblem {
    public static int f1(int n) {
        if (n < 1) {
            return 0;
        }
        if (n == 1 || n == 2) {
            return 1;
        }
        return f1(n - 1) + f1(n - 2);
    }

    public static int f2(int n) {
        if (n < 1) {
            return 0;
        }
        if (n == 1 || n == 2) {
            return 1;
        }
        int res = 1;
        int pre = 1;
        int tmp = 0;
        for (int i = 3; i <= n; i++) {
            tmp = res;
            res = res + pre;
            pre = tmp;
        }
        return res;
    }
    public static int f3(int n){
        if (n < 1) {
            return 0;
        }
        if (n == 1 || n == 2) {
            return 1;
        }
        int[][] base = new int[][]{
                {1,1},
                {1,0}
        };
        int[][] res = matrixPower(base, n - 2);
        return res[0][0] + res[1][0];
    }

    public static int[][] matrixPower(int[][] base,int p){
        int[][] res = new int[base.length][base[0].length];
        for (int i = 0; i < res.length; i++) {
            res[i][i] = 1;
        }
        int[][] t = base;
        for (; p!=0 ; p>>=1 ){
            if((p&1)!=0){
                res = product(res,t);
            }
            t = product(t,t);
        }
        return res;
    }

    public static int[][] product(int[][] a,int[][] b){
        int m = a.length;
        int k = b[0].length;
        int c = a[0].length;
        int[][] res = new int[m][k];
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < k; j++) {
                for (int l = 0;l < c; l++) {
                    res[i][j] += a[i][l] * b[l][j];
                }
            }
        }
        return res;
    }
//public static int[][] product(int[][] a, int[][] b) {
//    int n = a.length;
//    int m = b[0].length;
//    int k = a[0].length; // a的列数同时也是b的行数
//    int[][] ans = new int[n][m];
//    for(int i = 0 ; i < n; i++) {
//        for(int j = 0 ; j < m;j++) {
//            for(int c = 0; c < k; c++) {
//                ans[i][j] += a[i][c] * b[c][j];
//            }
//        }
//    }
//    return ans;
//}

    public static int s1(int n) {
        if (n < 1) {
            return 0;
        }
        if (n == 1 || n == 2) {
            return n;
        }
        return s1(n - 1) + s1(n - 2);
    }

    public static int s2(int n) {
        if (n < 1) {
            return 0;
        }
        if (n == 1 || n == 2) {
            return n;
        }
        int res = 2;
        int pre = 1;
        int tmp = 0;
        for (int i = 3; i <= n; i++) {
            tmp = res;
            res = res + pre;
            pre = tmp;
        }
        return res;
    }

    public static int s3(int n) {
        if (n < 1) {
            return 0;
        }
        if (n == 1 || n == 2) {
            return n;
        }
        int[][] base = { { 1, 1 }, { 1, 0 } };
        int[][] res = matrixPower(base, n - 2);
        return 2 * res[0][0] + res[1][0];
    }

    public static int c1(int n) {
        if (n < 1) {
            return 0;
        }
        if (n == 1 || n == 2 || n == 3) {
            return n;
        }
        return c1(n - 1) + c1(n - 3);
    }

    public static int c2(int n) {
        if (n < 1) {
            return 0;
        }
        if (n == 1 || n == 2 || n == 3) {
            return n;
        }
        int res = 3;
        int pre = 2;
        int prepre = 1;
        int tmp1 = 0;
        int tmp2 = 0;
        for (int i = 4; i <= n; i++) {
            tmp1 = res;
            tmp2 = pre;
            res = res + prepre;
            pre = tmp1;
            prepre = tmp2;
        }
        return res;
    }

    public static int c3(int n) {
        if (n < 1) {
            return 0;
        }
        if (n == 1 || n == 2 || n == 3) {
            return n;
        }
        int[][] base = {
                { 1, 1, 0 },
                { 0, 0, 1 },
                { 1, 0, 0 } };
        int[][] res = matrixPower(base, n - 3);
        return 3 * res[0][0] + 2 * res[1][0] + res[2][0];
    }

    public static void main(String[] args) {
        int n = 19;
        System.out.println(f1(n));
        System.out.println(f2(n));
        System.out.println(f3(n));
        System.out.println("===");

        System.out.println(s1(n));
        System.out.println(s2(n));
        System.out.println(s3(n));
        System.out.println("===");

        System.out.println(c1(n));
        System.out.println(c2(n));
        System.out.println(c3(n));
        System.out.println("===");

    }
}
